Sylvia, the narrator and protagonist of the story, seems to perceive Miss Moore as her antagonist in the story. As a child, she and her friend, Sugar, thought that everyone else was "old and stupid or young and foolish," and the girls thought that only the pair of them were "just right." Miss Moore, Sylvia says, moved into the neighborhood with "nappy hair and proper speech and no makeup," and so she and Sugar laughed at Miss Moore and "hated her too."
However, it soon begins to become clear that Sylvia's antagonist is not Miss Moore, a woman who is clearly trying to help to educate the children in the neighborhood about the world; rather, Sylvia's antagonist is the inequalities in society that account for Sylvia's parents' struggles, the poverty of her neighborhood, and the need Miss Moore feels to help these children who do not benefit from the racial and economic privilege enjoyed by others. Thus, the central conflict is of the character (Sylvia) vs. society variety.
Sugar says that this country "is not much of a democracy" because people do not have an "equal crack" at earning the money necessary to purchase luxury items (or even necessary items). Sylvia, however, does not come to such clear conclusions and understandings yet; instead, she says that she wants to go off by herself "to think this day through." She does, however, seem to recognize that she must fight the world, saying that "ain't nobody gonna beat [her] at nuthin." Thus, the conflict is not actually resolved at all but will continue for the entirety of her life unless incredible strides are made to make her society truly equal.